Ahmad is the top remaining target for government forces battling to end the almost five-month siege of Marawi that has claimed more than 1,000 lives and left the Islamic city in ruins.
"They're leaderless and they have no more organisation", he said.
Rumors of Hapilon and Maute's death have periodically circulated in the past but on Monday Philippine Defense Secretary Delfin Lorenzana confirmed the latest reports to the Philippine Daily Inquirer.
Evacuees chatted about the news and looked at Facebook posts showing pictures of the dead Hapilon and Maute. The other militant leader killed was Omar Maute, one of the two brothers who led the Maute terrorist group in the country, Lorenzana told a news conference. He said the fighting is nearing its end, but "We will take all the time we need so we can save whatever lives are still in the battle zone".
As the fight between the Philippine security forces and ISIS-linked terrorists in Marawi continues, state security officials reportedly announced that two key terror leaders were eliminated in a gunfight between the sides Monday morning.
Philippine military chief of staff General Eduardo Ano showed reporters a photo of what he said was Hapilon's bloodied face.
The Philippine government had offered a 10m Philippines peso bounty for Hapilon on top of the $5m reward offered by the US.
The siege, which lasted nearly five months destroyed much of the city's once popular center and left more than 400,000 people from Marawi and elsewhere living in temporary shelters.
Malaysian militant leader Mahmud Ahmad was still in Marawi, with authorities describing him as the "conduit" between IS and local militant groups.
The military's recent offensive led to the release of 17 hostages, according to Zia Alonto Adiong, spokesperson for the Marawi Crisis Management Committee. The restive south of the mainly Catholic Philippines is home to a decades-old Muslim separatist insurgency and to extremist gangs that have declared allegiance to IS including the Abu Sayyaf and Maute groups.
A Philippine military spokesman says troops are being careful in the intense fighting with militants in Marawi city because of concerns for the safety of the 50 to 100 hostages still being held by the Islamic State group-linked militants. "We just needed to get these two (leaders) to make sure the leadership, the centre of gravity falls, and elsewhere even the Maute-ISIS (fighters) in other areas would also crumble".